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From "Martin Desruisseaux (JIRA)" <>
Subject [jira] [Created] (SIS-155) Area calculation on ellipsoid
Date Wed, 18 Dec 2013 17:20:06 GMT
Martin Desruisseaux created SIS-155:

             Summary: Area calculation on ellipsoid
                 Key: SIS-155
             Project: Spatial Information Systems
          Issue Type: New Feature
          Components: Referencing
    Affects Versions: 0.3
            Reporter: Martin Desruisseaux

We need a method for calculating the area inside a polygon on the ellipsoid. An algorithm
working in Cartesian coordinate system is available there:


This algorithm can be adapted to spherical coordinate systems by replacing the area sum by
(note that this replacement uses vertical strips instead than horizontal ones):

s += (λ2 - λ1) * (2 + sin(φ1) + sin(φ2));

and the final answer by:

area = abs(s * r² / 2);

The _r_ value could be approximated to the authalic radius (the radius of a hypothetical sphere
having the same surface than the ellipsoid). However an article on
seems to use a more local approximation, where _a_ and _b_ are semi-major and semi-minor axis

s = sin(φ)
c = cos(φ)
r = (a²b) / (a²c² + b²s²)

This task just write down some ideas. We probably need to read the above-cited article and
other internet resources more carefully.

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